There are lots of project that can be developed using socket programming, As a matter of fact, developing projects is the best way of understanding and implementing the concepts and achieve a firm hold on the subject. Few projects that I can suggest and I will keep on updating the list every month.
1. Developing a Browser
2. Developing a HTTP Server
3. Developing a Chat Server

Few projects I can suggest from security implementation in Networks
1. Implementation of DES algorithm
2. Implementation of MD5 algorithm

All these projects require a thorugh understanding of C on Unix platform, especially structures and pointers. So brush up your skills on structures and pointers before starting with the project.